* Oil gains as Brexit fears ease
* Rough injection outage extended until Tuesday
* Gas system oversupplied by 34 mcm/day
June 20 (Reuters) - British wholesale gas prices rose on Monday, buoyed by a stronger oil market as fears of Britain voting to leave the European Union in a referendum on Thursday receded.
Gas for immediate delivery rose by 0.40 pence to 33.75 pence per therm at 0937 GMT, supported by gains further out on the curve, despite the gas system being oversupplied, traders said.
Contract for gas delivery next-month rose by 0.15 pence to 34.50 pence/therm, while the next-winter contract firmed by 0.61 pence to 41.25 pence/therm.
Oil extended gains on Monday as a weaker dollar and easing worries over Britain's possible exit from the European Union helped support crude prices.
"We expect increased volatility over the next few days as a result of Brexit," said Mehdi Khatibzadeh, gas trader at Wingas UK Limited.
"Demand has fallen significantly due to lower household consumption, but more importantly due to a continuation in the injection outage at Rough," a UK-based trader gas said.
Nominations into Britain's biggest gas storage site Rough were down to 1 mcm/day from 24 mcm/day on Friday as an injection outage was extended until Tuesday.
The day-ahead UK gas contract WAS 0.30 pence lower at 34.20 pence per therm.
In the Netherlands, the day-ahead gas price at the TTF hub rose by 0.38 euro per megawatt hour to 14.73 euro/MWh.
In the European carbon market, front-year allowances firmed by 0.13 euro to 5.80 euros a tonne. (Reporting by Nerijus Adomaitis and Nina Chestney)